Saturday, October 19, 2024

Swiss Micros DM32: Reimann-Louiville Fractional Integral of x^p

Swiss Micros DM32: Reimann-Louiville Fractional Integral of x^p


Introduction


The program presented today calculates the Riemann-Louiville integral of:


f(t) = t^p, where p is a real number.


The formula for this integral is:


cDx^(-v) = 1 / Γ(v) * ∫( (x – t) * t^p dt, t = c, t = x)

= ∫( ((x – t) * t^p) / (v -1)! dt, t = c, t = x)


I covered these type of integrals on my September 14, 2024 blog.


DM32 Program: Reimann-Louiville Fractional Integral of x^p


LBL F

INPUT C

INPUT X

INPUT V

INPUT P

FN= I

RCL C

RCL X

∫ FN d T

RTN


LBL I

RCL X

RCL- T

RCL V

1

-

y^x

RCL T

RCL P

y^x

×

RCL V

1

-

x!

÷

RTN



Here is a text version that can be transferred to a dm32 state file (fractionalintegralm.d32):

https://drive.google.com/file/d/1E-wUq4GW5dX06VZ-5WWwy7KRm3SN_uyq/view?usp=sharing



Examples


Run program F: XEQ F. Make sure that V > 0.


C

X

V

P

Result (FIX 5)

0

5

2

2

52.08333

1

6

3

3

385.41667

2

7

1.5

3

717.69103

0

1

1.75

4

0.05298


Source


Kimeu, Joseph M., "Fractional Calculus: Definitions and Applications" (2009).Masters Theses & Specialist Projects. Paper 115. http://digitalcommons.wku.edu/theses/115


Eddie


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